Question: Solve for $x$ and $y$ using elimination. ${-5x+2y = -2}$ ${-4x+y = -7}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-5x+2y = -2}$ $8x-2y = 14$ Add the top and bottom equations together. $3x = 12$ $\dfrac{3x}{{3}} = \dfrac{12}{{3}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-5x+2y = -2}\thinspace$ to find $y$ ${-5}{(4)}{ + 2y = -2}$ $-20+2y = -2$ $-20{+20} + 2y = -2{+20}$ $2y = 18$ $\dfrac{2y}{{2}} = \dfrac{18}{{2}}$ ${y = 9}$ You can also plug ${x = 4}$ into $\thinspace {-4x+y = -7}\thinspace$ and get the same answer for $y$ : ${-4}{(4)}{ + y = -7}$ ${y = 9}$